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Difference of Squares

One of the most important formulas on the GRE is the difference of squares:

x2 - y2 = (x + y)(x - y)
 

Caution: a sum of squares, x2 + y2 , does not factor.
 

Example:
If x ≠ ––2, then 8 x2-324x+8 =

(A) 2(x –– 2)
(B) 2(x –– 4)
(C) 8(x + 2)
(D) x –– 2
(E) x + 4
 

In most algebraic expressions involving multiplication or division, you won’’t actually multiply or divide, rather you will factor and cancel, as in this problem.

8x2-324x+8 =

by the distributive property ax + ay = a(x + y)

8x2-44x+2 =

by the difference of squares x2 - y2 =(x + y)(x - y)

8x+2x-24x+2 =

by canceling common factors

2(x –– 2)

The answer is (A).

 





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